Editor's note: The following review originally appeared in the
April 2003 issue of the Journal of Political Economy.

Introduction

Throughout the Middle Ages and well into the Renaissance,
monetary systems experienced a recurring coinage problem. In
systems that had coins with at least some intrinsic value (for
example, silver or gold), intermittent shortages of small change
occurred. Debasements and an influx of foreign coins often accompanied
these shortages.

Throughout this period, governments struggled to overcome this problem,
but without much success. Carlo Cipolla (Money, Prices, and Civilization
in the Mediterranean World, Fifth to Seventeenth Century, 1956,
p. 31) called the failure of governments to prevent these shortages
"the big problem of small change." Cipolla's observation
provides the motivation (and title) for Thomas J. Sargent and François
R. Velde's book.

The Big Problem of Small Change is an impressive piece of
scholarship that should be of interest to most economists, not just
to economic historians. It offers a coherent model of money that helps
explain a recurring problem that can arise with a commodity money
system and that provides the basis for understanding a solution to
this problem.

The motivation and the model

The recurring shortages of small change are one part of the motivation
for the book. The other is contained in Figure 2.1 (p. 16), which
shows the metallic content of small coins for six economic regions
over hundreds of years. Each region shows a similar pattern of intermittent
debasements, decreases in the amount of metal, of small-denomination
silver coins from as far back as 1200 and extending to 1800. Sargent
and Velde (p. 15) interpret this as a "pervasive and persistent
depreciation of small denomination coins."

What do shortages have to do with depreciations? Or as Sargent and
Velde (p. 15) state the question, "How can something in short
supply have its price fall over time?" The first part of their
book presents a coherent model of money that provides an answer. The
fact that small coins are in short supply implies that they are providing
a liquidity service that large coins are not. Consequently, when a
small-coin shortage occurs, small coins have to depreciate relative
to large coins if the public is going to be willing to hold both.
This is the key insight in Sargent and Velde's research and underlies
much of their analysis.

More explicitly, the Sargent-Velde model is a variation of the conventional
cash-in-advance model of money. In it, there are two types of coins
of the same metal (say, silver). One contains a small amount; the
other, a large amount. Only small-denomination coins can be used in
small transactions (what Sargent and Velde call the "penny-in-advance
constraint"), but both denominations can be used in large transactions.

Both types of coin are minted freely (in the sense of unlimited, not
necessarily costlessly). The public brings an ounce of metal to be
minted and receives a set number of coins of a given type in return.
The intrinsic value of a coin in terms of goods is its mintequivalent. The mint equivalent less any government fees (seigniorage
and brassage) is the mint price.

The relationship between the price level (coins per consumption good),
the mint price and the mint equivalent determine whether a given coin
will be minted or melted. If the price level is less than the mint
price, the public has an incentive to turn its silver into coin. If
the price level exceeds the mint equivalent, the public has an incentive
to melt coins, turning them back into silver. As long as the price
level is less than its mint equivalent but greater than its mint price,
a given coin will be neither melted nor minted. In effect, each denomination
of coin has pairs of "silver points." Sargent and Velde's
model highlights the tendency for these silver points to become misaligned
as the economy grows or shrinks, creating shortages of some denominations
of coins.

The intermittent shortage theorem for small coins follows directly
from this model. If income should start increasing, the penny-in-advance
constraint can become binding, which is Sargent and Velde's definition
of a shortage. A shortage, in turn, implies that the return
on small-denomination coins must be less than that on large-denomination
coins; that is, the exchange rate of small for large coins must be
rising. Otherwise, no one will want to hold the large-denomination
coin. And a depreciating exchange rate can lead to a rising price
level (assuming that the small-denomination coin is the unit of account).
Further, if small coins depreciate to the extent that they become
worth more as a commodity than as a money, then they will be melted,
aggravating the shortage.

A government can eliminate the small-change shortage by debasing the
small coins. Thus, according to Sargent and Velde's model, most debasements
were benign governments' cure for this recurring problem, rather than
avaricious governments' means to collect seigniorage.

Confronting the data

The first section of the book provides a general overview of the
facts motivating the study and the theory that will be used to explain
the facts. This is followed by a section of three extensively researched,
but loosely connected, chapters. The first, Chapter 4, is a history
of the evolution of the minting technologies that eventually mitigated
the counterfeiting problem enough to allow for convertible token coins.
Chapters 5 and 6 are two engaging chapters that go through hundreds
of years of the history of legal and economic thought on the value
of metal coins.

In these latter two chapters, Sargent and Velde trace the evolution
of the valuation of coins through the Middle Ages in legal contracts.
The prevailing view in 1200 was that coins should be valued by their
metal content. By 1600 this view had evolved to admit the theoretical
and practical possibilities that coins could be valued by tale, that
is, simply by count. The distinction is important in Sargent and Velde's
theoretical model, which, like other models of Sargent and Smith (Journal
of Economic Theory, 1997) and Velde and Weber (Journal of Political
Economy, 2000), assumes that coins exchange by tale and above
their intrinsic value.

The theory is confronted with the historical evidence in the third
section of the book. This section is most impressive because the evidence
covers several city-states and countries over a long historical period
and consists of data on mint prices, mint equivalents, exchange rates
between coins, prices and minting volumes. In general, Sargent and
Velde find the evidence to be consistent with the theory.

The section begins with the establishment of the relevant facts: Depreciations,
debasements and the influx of foreign coins accompanied intermittent
shortages of small-denomination coins. For example, Chapter 8 demonstrates
that small-change shortages were recurring in medieval England and
France. Here the authors present anecdotal evidence from contemporary
writers complaining of shortages. They support this evidence with
examples of government interventions that are also evidence of small-change
shortages. These examples include restrictions on the import of foreign
coins that had lower intrinsic content, prohibitions on the export
of domestic small coins, the introduction of new, lower-valued coins
(England) and requirements to mint small coins (France). Presumably,
a lack of price-level and exchange-rate data prevented Sargent and
Velde from using these examples to test their theory.

The next chapters look at the history of coinage in Italy and France
to determine if it is consistent with the implications of their model
once a shortage occurs. Chapter 9 discusses coinage evidence from
Florence roughly over the period from 1250 to 1500. As predicted by
the theory, piccioli and quattrini, the small-denomination coins,
depreciate against the large-denomination silver and gold coins. The
largest part of the chapter is spent discussing the period from 1330
to 1380, which includes the so-called Quattrini affair. This experience
generally accords well with the predictions of the model. The price
level and the exchange rate move together for most of the period.
However, the authors note an exception. The upward movement in prices
roughly between 1365 and 1370 precedes the movement of the exchange
rate, rather than being coincident with it as the model would predict.
Chapter 10 discusses similar evidence for Venice for roughly the same
period. As was the case in Florence, the piccioli depreciate against
the large-denomination silver and gold coins as predicted by the theory.
Unfortunately, the lack of price-level data prevents Sargent and Velde
from testing this implication of their theory with data from Venice.

Chapter 11 discusses the shortage evidence for France in the 15th
through the 17th centuries. The primary focus is on the 1500s. Extensive
evidence on the existence of small-change shortages is presented,
and the authors show that small-denomination coins depreciated against
large-denomination ones.

A disappointing aspect of this section is that the authors do not
make greater use of the minting data they have. Data on mint bounds,
prices and minting quantities are presented for both the Quattrini
affair (Florence) and France. However, Sargent and Velde make no attempt
to see if the minting data conform to the model's prediction that
a coin should be minted whenever its mint price equals the price level.
At least for Florence, our impression is that this prediction of the
model would be borne out by the minting data.

Discovering the standard formula and lessons learned about fiat money

A solution to the small-change problem is the standard formula.
It calls for eliminating the free minting of small-denomination coins.
In their place, the government issues token coins (small-denomination
coins that have little or no intrinsic value) that are convertible
into something that has intrinsic value.

Sargent and Velde argue that once their theory is understood, the
standard formula solution is obvious. The convertibility of the token
coins eliminates the penny-in-advance constraint that is the source
of the big problem of small change. However, most countries only adopted
the standard formula in the late 1800s after centuries of trial and
error.

In the fourth section of the book, Sargent and Velde examine why it
took "historical decision makers" so long to discover the
standard formula solution. In particular, they investigate whether
the delay was caused by the lack of a technology for making token
coins that were difficult to counterfeit or whether it was caused
by governments having to learn why money is valued. They conclude
that both causes played a role in delaying the adoption of the standard
formula.

The heart of this section is the chapters that describe several experiments
with small change. Sargent and Velde allege that these experiences
provided historical decision makers with theory and evidence leading
to the standard formula as the solution to the small-change problem.

One of these experiments, described in Chapter 14, is the 17th-century
Castilian experiment with inconvertible copper coins. By royal decree
in 1596, a limited quantity of new small-denomination, inconvertible,
pure copper coins were to be minted to replace the existing partly
silver small coins. Sargent and Velde document that for roughly 40
years, this copper coinage circulated above its intrinsic value, that
is, by tale rather than by weight. By 1626, so much of this copper
coinage had been emitted that all the large-denomination, pure silver
coins had been replaced. Sargent and Velde assert that inflation set
in at this point. (Strangely, they discuss inflation in terms of the
exchange rate between copper and large silver coins, which presumably
no longer were around, rather than in terms of the price of consumption
goods and copper coins.) After the king abruptly halted the minting
of copper coins, the inflation abated. Sargent and Velde argue that
this experiment revealed that coins could circulate by tale so that
the quantity of money determined the price level and that convertibility
was important for implementing the standard formula.

Another of these experiments is the way Britain dealt with small change
from the mid-1500s to 1817. At times during this period, the government
permitted private laissez-faire provision of copper coins. These coins
were convertible. During one of these periods, the private coins solved
the small-change shortage to such an extent that Sir Henry Slingsby,
master of the London Mint, stated something very close to the standard
formula in 1661. Despite Slingsby's statement and the availability
of a new technology that would make tokens more difficult to counterfeit,
Britain did not adopt the standard formula officially for another
150 years. And that adoption was "accidental," in the sense
that it nationalized the private copper coinage system that had been
in place since the 1740s. The authors blame the delay on John Locke's
argument that all coins should be full-bodied and the fact that a
convertibility commitment by the Stuart kings might not have been
believed.

As Sargent and Velde document, the discovery and acceptance of the
standard formula was anything but linear. Nevertheless, there is no
reason to doubt their claim that the benefits of the standard formula
were uncovered through these experiments and eventually led to its
adoption.

There is reason, however, to question the authors' claim about what
was learned about fiat money. According to Sargent and Velde (p. 330),
"The evolution of monetary doctrines about small change was an
important part of the process by which a managed fiat currency system
came to be understood and implemented." The authors present no
direct evidence that policymakers gleaned such insights from this
history. Instead, their presumption is that since it was learned that
a commodity money could circulate above its intrinsic value, it was
learned that a fiat money (a money that is intrinsically worthless
and irredeemable) could as well. This presumption is not obvious.
Even in the late 1800s to early 1900s, policymakers and leading
academics were still debating whether money's quantity or its intrinsic
value determines its value. [See, for example, the following in the
Journal of Political Economy: H. Parker Willis (1896), J. Laurence
Laughlin (1903) and Spurgeon Bell (1906).] Further, it is not apparent
that the lessons of the Castilian inflation were learned when countries
adopted fiat money systems. As Sargent and Velde (p. 14) themselves
admit, "The twentieth century brought many prolonged inflation
experiments with fiat money."

Concluding comments

Despite our quibbles, The Big Problem of Small Change is
a remarkable book. The history of small-change shortages alone should
be required reading for monetary economists and economic historians.
Furthermore, the authors' use of an economic model to confront the
small-change problem should be of interest to the general profession
as well as to theorists. For those pursuing future historical research,
we think that Sargent and Velde's use of a model to examine a historical
puzzle will be a productive methodology for both testing economic
theories and understanding economic history.